To find the median of the given data set, we first need to arrange the numbers in ascending order (which they already are):
1, 1, 2, 2, 4, 6, 6.8, 7.2, 8, 8.3, 9, 10, 10, 11.5
Next, we count the number of observations in the data set. There are 14 numbers in total.
Since the number of observations (n) is even (n = 14), the median is calculated as the average of the two middle numbers. The two middle numbers in this case are the 7th and 8th numbers:
7th number: 6.8
8th number: 7.2
Now, we calculate the median:
\[ \text{Median} = \frac{6.8 + 7.2}{2} = \frac{14}{2} = 7 \]
Thus, the median of the data set is 7.